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An Electron Force Field for Simulating Large Scale Excited Electron Dynamics

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An Electron Force Field for Simulating Large Scale Excited Electron Dynamics An electron force ¯eld for simulating large scale excited electron dynamics Thesis by Julius T. Su In Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2007 (Defended April 12, 2007) ii °c 2007 Julius T. Su All rights Reserved iii Acknowledgements I dedicate this thesis to my parents. I thank them for teaching me early, teaching me well, and indulging and nurturing my curiosity about the world until it became self-sustaining. My brother Jonathan and sisters Judy and Jessica have always been there for me as well, and we have had a good journey together. It has been a pleasure to work for my advisor, Prof. Bill Goddard, who attacks scienti¯c problems with great enthusiasm, open-mindedness, and a formidable arse- nal of ideas and approaches. His way of getting to the root of things and identifying the key experiment that needs to be done is as reflexive for him as breathing. I appreciate that Bill gave me the freedom to work on many di®erent projects, and his level of expertise and broad range of interests was such that he provided good insights on every one of them. The stimulus behind the electron force ¯eld and this thesis was the ideas presented in his Nature of the Chemical Bond course { he talked about electrons moving around and \pooching", changing in size and becoming orthogonal to each other, and his level of enthusiasm motivated me to develop a simulation of these events happening. I also had the privilege to work with Prof. Brian Stoltz for nearly a year on developing the Wol®/Cope reaction. He is a great experimentalist, and I was humbled that he was willing to entrust the initial development of his reaction to a ¯rst year graduate student. I appreciated his hands-on guidance and attention to detail. After I joined Bill's group, I continued to do theory on the reaction while Richmond Sarpong took over and made great strides in the experimental work, continued later by Jenny Roizen; it was a very successful division of labor. Prof. Ahmed Zewail introduced me to computational chemistry as an under- graduate in the context of modeling caging of charge-transfer reactions in clusters. I am indebted to him for his support and encouragement, his scienti¯c and per- sonal insights, and his ¯rm insistence that I learn the theory behind every part of my calculations properly. I appreciate the time he spent with our project, and the interest he took in making sure I developed well as an independent researcher. iv Prof. Thomas Tombrello was responsible for starting me on scienti¯c research at Caltech as an undergraduate through the Physics 11 program. My other thesis committee members, Prof. Rudy Marcus and Prof. Harry Gray, have provided me with useful insights and guidance through the candidacy, pro- posal, and thesis defense stages, and I thank them. Prof. Bruce Hay, though not formally involved with my graduate work, has always made time to talk with me about science and non-science, and I value our friendship. I have made wonderful friends at Caltech, who made my days happier and brighter, and I hope I did the same for them { I thank Victor Kam, Sam Cheung, Yen Nyugen, Xin Zhang, Santiago Solares, Jiyoung Heo, and Robert Bao. John Keith was responsible for especially entertaining political discussions as well. Finally I thank Tim for his love and steadfast support, especially during the time of thesis writing. I hope that the successful completion of my thesis will begin to make up for the time we have spent apart. v An electron force ¯eld for simulating large scale excited electron dynamics by Julius T. Su In Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy Summary Much interesting chemistry involves the motion of large numbers of excited elec- trons, yet theory is limited in its ability to simulate such systems. We introduce an electron force ¯eld (eFF) that makes simulation of large scale excited electron dynamics possible and practical. The forces acting on thousands of electrons and nuclei can be computed in less than a second on a single modern processor. Just as conventional force ¯elds parameterize the ground state potential be- tween nuclei, with electrons implicitly included, electron force ¯elds parameterize the potential between nuclei and simpli¯ed electrons, with more detailed degrees of freedom implicitly included. The electrons in an electron force ¯eld are Gaussian wave packets whose only parameters are its position and its size. Using a simple version of the electron force ¯eld, we compute the dissocia- tion and ionization behavior of dense hydrogen, and obtain equations of state and shock Hugoniot curves that are in agreement with results obtained from vastly more expensive path integral Monte Carlo methods. We also compute the Auger dissociation of hydrocarbons, and observe core hole decays, valence electron ion- izations, and nuclear fragmentation patterns consistent with experiment. Despite the simplicity of the electron representation, with a judicious choice of potentials we are able to describe electrons of di®erent shapes in di®erent environ- ments. vi In one chapter, we show we can describe p-like valence electrons using spherical Gaussian functions, enabling us to compute accurate ionization potentials and po- larizabilities for ¯rst row atoms, and accurate dissociation energies and geometries of atom hydrides and hydrocarbons. In another chapter, we show that we can describe delocalized electrons in a uniform electron gas using localized eFF orbitals. We reproduce the energy of a uniform electron gas, including correlation e®ects; and following the historical development of density functional theory, we develop a preliminary eFF that can compute accurate exchange and correlation energies of atoms and simple molecules. In the following pages, we have highlighted successes of eFF, but have not shied away from analyzing in depth areas where it could be improved. We hope that this combination of promising results and critical analysis stimulates and assists further research in this exciting ¯eld. vii Contents 1 The electron force ¯eld, a method for simulating large-scale ex- cited electron dynamics 1 2 Development of an electron force ¯eld. I. Low Z atoms and hy- drocarbons, and matter at extreme conditions 25 3 Development of an electron force ¯eld. II. New treatment of p- like electrons, resulting in improved accuracy for ¯rst-row atoms, atom hydrides, and hydrocarbons 89 4 Development of an electron force ¯eld. III. Metallic electrons and the uniform electron gas. Creation of a correlation function 133 viii List of Figures 1.1 Excited condensed state electrons drive essential chemistry. 2 1.2 Electron force ¯eld makes feasible simulations of large scale excited electron dynamics. 3 1.3 (a) Excited condensed system evolves through many curve cross- ings, and can be approximately described by a mean ¯eld trajec- tory. (b) However, the mean ¯eld trajectory may incorrectly bisect well-separated adiabatic states. 8 1.4 Summary of electron force ¯eld development. 12 1.5 Character of electron depends on its proximity to nuclei. 12 1.6 Gaussian and exact wave packet dynamics match for free particle and harmonic oscillator potentials. 15 1.7 Exact and Gaussian wave packet dynamics for a double well potential. 16 1.8 In sparse systems, electrons move mostly along adiabatic paths, with crossings limited to conical intersections with reduced dimensionality. 19 2.1 H2 potential energy surface (kcal/mol); eFF properly dissociates H2, but the simplicity of the basis leads to underbinding. 31 2.2 Pauli repulsion comes from the kinetic energy increase upon making orbitals orthogonal to each other. 33 2.3 Comparison of Pauli repulsion and electrostatic repulsion between two wavefunctions with s = 1. 35 2.4 eFF geometries of simple substituted hydrocarbons . 36 2.5 eFF geometries of larger hydrocarbons, bond lengths in Angstroms 37 ix 2.6 Multiple bonds can split σ ¡ ¼ or form symmetric \banana" pairs. 38 2.7 eFF reproduces curved bonds of cyclopropane, and pucker of ¯ve and six membered rings. 41 2.8 eFF reproduces steric repulsions within alkanes . 42 2.9 eFF reproduces allylic strain interaction . 43 2.10 In eFF, methyl cation and radical are stable but methyl anion is unbound . 44 2.11 Protonation of helium and ammonia . 47 2.12 Carbocations can rearrange via hydride or methyl shifts. 48 2.13 eFF distinguishes between allowed and forbidden hydrogen reactions. 48 2.14 eFF can account for ionic and multicenter bonding. 50 2.15 Previously proposed plasma phase transition [42, 43] where hydro- gen dissociates and ionizes simultaneously . 53 2.16 Dynamics snapshots showing deuterium dissociation as temperature is raised. 55 2.17 Proton-proton pair distribution function shows gradual dissociation. 56 2.18 Equation of state (rs = 2 bohr) shows good agreement with best available theory. 57 2.19 High densities suppress ionization that occurs at high temperature. 58 2.20 Reproduction of the experimental shock Hugoniot curve obtained by gas gun and Z machine; Nova laser remains an outlier. 60 2.21 Core holes relax via a two stage Auger decay process. 61 2.22 Red points compare Boys localized Hartree-Fock orbital energies to eFF orbital energies. 63 2.23 Removal of valence electrons from ethane results in selective bond breaking. 64 2.24 Electron energies show Auger process in adamantane in detail. 66 2.25 Auger dissociation of methane and ethane following creation of a core hole. 69 x 2.26 Auger dissociation of neopentane and adamantane following cre- ation of a core hole. 72 2.27 We remove a core electron from a central carbon of a diamondoid particle.
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